Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#import<cstdio>

int N, d[8 << 15], p[8 << 15], x, i;

int main(){
    scanf("%d", &N);
    for(; i < N; d[x] = ++i)
        scanf("%d", &x);
    x = N;
    for(; --i; p[i] += p[i + 1])
        if(p[i + 1]){
            if((d[i] < d[i + 1]) ^ (d[i + 1] < d[x]) ^ (d[x] < d[i])){
                ++p[i];
                x = i + 1;
            }
        }else
            if(d[i] < d[i + 1])--x;
            else++p[i];
    printf("%d", p[1]);
}